Investigation on thermoelastic vibration of FG multilayer hybrid nanocomposite microbeam reinforced by CNTs and GPLs under nonlocal strain gradient elasticity and three-phase-lag generalized thermoelastic theory

Abstract

In recent years, extensive studies on carbon nanotubes-reinforced composites (CNTRC) and graphene platelets-reinforced composites (GPLRC) have been conducted primarily within the framework of the classical elasticity or thermoelasticity. With the development of micro/nano devices, the study of thermoelastic vibration and size-dependent effects in variable temperature environments is becoming more and more important. There is a notable absence of studies examining the thermoelastic behaviors of graphene platelets reinforced composite (GPLRC) or carbon nanotubes reinforced composite (CNTRC) structures within the framework of generalized thermoelasticity that considers non-Fourier heat conduction, particularly regarding the microstructures of CNTRC/GPLRC materials that require consideration of nonlocal effects. To address this gap, this study examines the thermoelastic vibration characteristics of a nanocomposite microbeam reinforced with both CNTs and GPLs within the framework of nonlocal strain gradient elasticity theory and the three-phase-lag (TPL) generalized thermoelastic theory for the first time. The Halpin–Tsai micromechanical model is employed to determine the effective elastic modulus of the composite microbeam. Subsequently, the problem is formulated using the Euler–Bernoulli beam model, and the resulting governing equations are solved using Navier’s method to derive the natural frequency. In calculation, besides unidirectional pattern for CNTs and GPLs, three different functionally graded (FG) distribution patterns, i.e., FG-A type, FG-X type, and FG-O type, are considered. Concurrently, the study evaluates the impacts of key factors including characteristic length parameters, surface effects, nonlocal parameters, volume fraction indices, and mass fractions of CNTs and GPLs on the natural frequencies. The results show that the dimensionless natural frequency of the FG-X type microbeam is approximately 26% higher than that of the UD type and 41% higher than that of the FG-A type. When the nonlocal parameter increases from 0 to 0.2, the natural frequency decreases by approximately 15–20%, while the strain gradient parameter increases it by 60–80%. Surface effects, mass fractions, and volume fraction index all positively correlate with the natural frequency.